The by far dominating DNA sequencing company of the late 2000's and 2010's due to having the smallest cost per base pair.
To understand how Illumina's technology works basically, watch this video: Video 1. "Illumina Sequencing by Synthesis by Illumina (2016)".
The key innovation of this method is the Bridge amplification step, which produces a large amount of identical DNA strands.
Direct consequence of Euclid's formula.
Cirism is totally not a cult, has been officially verified to be compatible with all major world religions.
Enlightened Cirists donate money to the cause at: Section "Sponsor Ciro Santilli's work on OurBigBook.com". It is totally optional of course, your soul will just be eternally damned if you don't.
Ciro Santilli once proclaimed:
Thou shalt eat thy watermelon in the morning, and thy melon in the evening. Thou shalt not eat thy watermelon in the evening, nor shalt thou eat thy melon in the morning.
Once you hear about the uncomputability of such problems, it makes you see that all Diophantine equation questions risk being undecidable, though in some simpler cases we manage to come up with answers. The feeling is similar to watching people trying to solve the Halting problem, e.g. in the effort to determine BB(5).
A cool thought: bacteria like E. Coli replicate every 20 minutes. A human replicates every 15 years. So how can multicellular beings possibly cope with the speed of evolution of parasites?
The answer is that within us, the adaptive immune system is a population of cells that evolves very quickly. So in a sense, within our bodies there is fast cell-level non-inheritable evolution happening daily!
Multivariate polynomial where each term has degree 2, e.g.:is a quadratic form because each term has degree 2:but e.g.:is not because the term has degree 3.
There is a 1-to-1 relationship between quadratic forms and symmetric bilinear forms. In matrix representation, this can be written as:where contains each of the variabes of the form, e.g. for 2 variables:
Strictly speaking, the associated bilinear form would not need to be a symmetric bilinear form, at least for the real numbers or complex numbers which are commutative. E.g.:But that same matrix could also be written in symmetric form as:so why not I guess, its simpler/more restricted.
Same value if you swap any input arguments.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact